fisherka wrote:
How do you measure sky brightness in magnitudes per square arcsecond
(MPSA)? Is there some way to relate this measurement to the more
typical zenith limiting magnitude or limiting magnitude of the
observing field?

Bill Ferris' article in this month's Sky and Telescope on Optical
Detection Magnitude (ODM) provides a reference to Bartel's c-code
software to compute the ODM. (
http://www.efn.org/~mbartels/aa/visual.html )

One of the input parameters for this model for the visibility of
extended objects is the background brightness of the sky measured in
magnitude per square arcsecond (MPSA).

I am unable to relate this parameter to my existing knowledge of the
limiting magnitude of the observing field, so I can make estimates of
the MPSA during my observing sessions.

Some of the background internet references related to the article
suggest values like:

Mount Wilson 19.8
Palomar Mountain 21.5
Lick Obs. 20.7
Mount Lemmon 21.5 (near Tucson)
Lowell (Mars Hill) 20.5
Van Vleck 18.7 (Connecticut)
David Dunlap 18.4 (Toronto)
Haute Provence 21.8 (southern France)

Any help on how to estimate the MPSA during my local observing
sessions would be appreciated.

One of the challenges I've been mulling over is finding a way to convert a
naked eye limiting magnitude estimate to a sky surface brightness value. It's a
challenge because, even among a group of experienced observers, naked eye
limiting magnitude estimates can vary significantly. See Bradley Schaefer's
1990 PASP paper for an illustration of this:

http://adsbit.harvard.edu/cgi-bin/np...=1990PASP..102
...212S&db_key=AST&page_ind=0&plate_select=NO&data _type=GIF&type=SCREEN_GIF

At best, I suspect such a conversion would get an observer in the ballpark,
perhaps to within 0.5 magnitude. Here's a table I'll throw out for commentary.
I'd be interested in hearing how well this reflects the real life experiences
of other observers:

NELM.(+/- 0.5)..===..Sky Brightness (mag./sq. arc sec.)
........8.0............22.0
........7.0............21.0
........6.0............20.0
........5.0............19.0
........4.0............18.0

The scale assumes a naked eye limiting magnitude of 8.0 (+/- 0.5) under a dark
country sky and a logarithmic relationship between sky brightness and NELM: for
every full magnitude change in sky brightness, there is a full magnitude change
in NELM.

The faint limit is actually well-established. The darkest the sky gets anywhere
on the planet is 22.0 mag. per sq. arc second. Observers with acute vision have
been known to go as faint as about 8.0 mag. (+/- 0.5 mag., depending on the
observer) under such conditions. Hence, the choice of an NELM of 8.0 with a +/-
0.5 magnitude range for a truly pristine sky.

The sky surface brightness over Mars Hill on the west side of Flagstaff,
Arizona, has been measured by Brian Skiff at 20.3 magnitude per square arc
second on a moonless, clear night. His NELM from this site is about 6.4
magnitude. It's only one data point but it falls within the NELM range for a
sky brightness of 20.0 mag. per sq. arc second.

A sky brightness of 18.0 mag. per sq. arc second corresponds to conditions at
Mars Hill during full Moon. From my home in north-central Flagstaff, about 3
miles east of Mars Hill, I can still see most of the stars in the Little Dipper
asterism under a full Moon. Also from home, I've seen M44 (3.1 mag, 95'
diameter) with the full Moon just 25-degrees away in Leo. A naked eye limit 4.0
magnitude (+/- 0.5) seems a reasonable choice for a bright sky with an 18.0
mag. per sq. arc second surface brightness.

You can also use Bartels' ODM program to explore this. Go back through your
observing records and find the most difficult visual detections of galaxies.
You can go to the NASA/IPAC Extragalactic Database (NED:
http://nedwww.ipac.caltech.edu/ ) to find magnitude and size data for the
galaxy. Enter those numbers and the aperture of your telescope in ODM. Then,
experiment with a range of sky surface brightness numbers to see where the
cutoff is for detection.

Keep in mind that an object at the very threshhold of detection may be visible
only 30% of the time or so with averted vision. In other words, if the objects
you're using to test ODM were visible with direct vision pretty much all the
time, then the LCD (Log Contrast Difference) will probably be 0.25 or greater.

Here's a recent example from my observations. MCG +7-34-50 is a 14.8 magnitude
galaxy near NGC 6166. I observed this object about three weeks ago from a true
dark sky site with my 10-inch Newtonian. Its small size, about 0.4'x0.4',
yields a quite reasonable surface brightness of 21.6 MPSA. At high
magnification, this little stinker was visible with averted vision about 40% of
the time.

Using the above numbers and a sky brightness of 22.0 MPSA, ODM predicts an
object of this type would be visible with an LCD of 0.09. Increasing the sky
brightness to 21.5 MPSA, the LCD drops to 0.02, indicating an object at the
very threshhold of visibility. The site I use is probably not perfect but,
taking into consideration photometry for the Lowell research site several miles
to the north, should fall somewhere around 21.8 MPSA.

I'd cite this as an observation which tends to confirm ODM's efficacy as a tool
for testing your observing site.

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
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